Born in Mostar, Bosnia and Herzegovina, Bogdanović started his basketball career in 2004 with his hometown club Zrinjski Mostar where he played for one season. In 2005, he signed a five-year deal with Real Madrid, but was loaned back to Zrinjski Mostar for the 2005–06 season. In 2006–07 and 2007–08, he played for Real Madrid's junior team, Real Madrid B, in Spain's 4th-tier league, the Liga EBA. In 2008, he was loaned to CB Murcia for the 2008–09 season. In January 2009, he re-joined Real Madrid's junior team, Real Madrid B. Following the 2008–09 season, he parted ways with Real Madrid.[1]

In August 2009, Bogdanović signed a four-year deal with Cibona Zagreb.[1] In July 2010, he signed a three-year contract extension with Cibona.[2] Following the 2010–11 season, he parted ways with Cibona.[3]

On June 19, 2011, Bogdanović signed a multi-year deal with Fenerbahçe Ülker.[4] On 23 June 2011, he was selected with the 31st overall pick in the 2011 NBA draft by the Miami Heat. He was later traded to the Minnesota Timberwolves, and then again to the New Jersey Nets on draft night.[5][6]

In September 2012, Fenerbahçe confirmed Bogdanović would return for the 2012–13 season.[7] In July 2013, following a breakdown in negotiations with the Brooklyn Nets on a possible contract buy-out, Bogdanović announced his decision to return to Fenerbahçe for the 2013–14 season.[8]

On July 20, 2014, Bogdanović signed a three-year, $10 million contract with the Brooklyn Nets.[9][10] After starting the first 19 games of the 2014–15 season alongside Joe Johnson on the wing, Bogdanović lost his starting spot on 10 December against the Chicago Bulls in favor of Sergey Karasev.[11] He later regained his starting spot on 10 January against the Detroit Pistons.[12] In the Nets' regular season finale on April 15 against the Orlando Magic, Bogdanović had a season-best game with 28 points on 12-of-17 shooting to help the Nets clinch the No. 8 seed in the Eastern Conference with a 101–88 win.[13] The Nets lost to the Atlanta Hawks 4–2 in the first round of the playoffs.

On November 11, 2015, Bogdanović helped the Nets record their first win of the season, scoring a season-high 22 points in a 106–98 victory over the Houston Rockets.[14] He topped that season high mark with 24 points on 25 February 2016 in a 116–106 win over the Phoenix Suns.[15] On March 15, 2016, he scored a career-high 44 points in a 131–114 win over the Philadelphia 76ers. His total was the most for a Nets player since Deron Williams scored 57 on March 4, 2012, and the most by any Nets player since the team moved to Brooklyn prior to the 2012–13 season.[16] In the Nets' regular season finale on 13 April, he tied his career high with seven three-pointers and scored 29 points in a 103–96 loss to the Toronto Raptors.[17] The Nets lost their final 10 games of the season and finished with a 21–61 win/loss record.

In the Nets' season opener on October 26, 2016, Bogdanović scored a team-high 21 points in a 122–117 loss to the Boston Celtics.[18]

On February 22, 2017, Bogdanović was traded, along with Chris McCullough, to the Washington Wizards in exchange for Andrew Nicholson, Marcus Thornton and a 2017 protected first round draft pick.[19] On March 1, 2017, he had a 27-point effort in a 105–96 win over the Toronto Raptors.[20] Four days later, he scored 15 of his 27 points and made five of his career-high eight three-pointers, including the game-winner, during the fourth quarter of the Wizards' 115–114 win over the Orlando Magic.[21] On March 7, he scored 29 points and set a franchise record for free throws made by going 16 of 16 in a 131–127 win over the Phoenix Suns.[22]

On July 10, 2017, Bogdanović signed with the Indiana Pacers.[23] In his debut for the Pacers in their season opener on October 18, 2017, Bogdanović scored 14 points in a 140–131 win over the Brooklyn Nets.[24] On February 5, 2018, he scored a season-high 29 points in a 111–102 loss to the Washington Wizards.[25] On March 5, 2018, he tied his season high with 29 points in a 92–89 win over the Milwaukee Bucks.[26] In Game 3 of the Pacers' first-round playoff series against the Cleveland Cavaliers, Bogdanović scored 19 of his playoff career-high 30 points in the second half, finishing 7 of 9 on 3-pointers, in a 92–90 win that saw the Pacers take a 2–1 lead.[27] The Pacers went on to lose the series in seven games.